Question: Chloe has enough sand to fill a rectangular sandbox with an area of $36$ square units. She wants the outer edges of the sandbox to use as little material as possible. Which dimensions will give Chloe the smallest perimeter? Choose 1 answer: Choose 1 answer: (Choice A) A $9$ units by $4$ units (Choice B) B $12$ units by $3$ units (Choice C) C $6$ units by $6$ units
Solution: Let's find the perimeter of each rectangle to see which one has the smallest perimeter. $\text{Perimeter} = \text{length} + \text{width} + \text{length} + \text{width}$ $6$ units by $6$ units $6\text{ units}$ $6\text{ unit}$ $$ $6\text{ units}$ $6\text{ units}$ $\text{Perimeter}={6}\text{ u}+6\text{ u} + {6}\text{ u}+6\text{ u} = 24\text{ units}$ $9$ units by $4$ units $9\text{ units}$ $9\text{ units}$ $$ $4\text{ units}$ $4\text{ units}$ $\text{Perimeter}={9}\text{ u}+4\text{ u} + {9}\text{ u}+4\text{ u} = 26\text{ units}$ $12$ units by $3$ units $12\text{ units}$ $12\text{ unit}$ $$ $3\text{ units}$ $3\text{ units}$ $\text{Perimeter}={12}\text{ u}+3\text{ u} + {12}\text{ u}+3\text{ u} = 30\text{ units}$ $24\text{ u} < 26\text{ u}< 30\text{ u}$ A rectanglar sandbox with the dimensions of $6\text{ units}$ by $6\text{ units}$ has the smallest perimeter.